Put the flour, green egg foam, oil, and salt in the bowl of a food processor. With the machine running, drizzle in the water. The mixture will first look flaky and then start to come together into a dough. Stop the processor after about 1 minute, when the dough is slightly crumbly but
holds together when you press it between your fingers.
Set the dough on the floured work surface and knead it for a few minutes, forming a smooth round ball. (It should be tacky to the touch. If it crosses the line into stickiness, add more flour, 1 tablespoon at a time.
Conversely, if it’s dry and won’t hold together, add water 1 tablespoon at a time.) Wrap the dough ball in plastic wrap and let it rest in the refrigerator for about 1 hour. (If you’re rolling the pasta by hand, let it rest on the counter instead of in the fridge; it’ll be easier to handle.)
Cut the dough in half and flatten each half with a rolling pin. Using a pasta machine or a stand mixer’s pasta attachment, roll it through a few times on the thickest setting. If the dough is sticking, add a bit more flour. When it holds together in a well-shaped rectangle and is flattened to about ¼ inch, turn up the settings according to your machine’s directions for ravioli and fettuccini (I use setting #4 on my KitchenAid attachment) and continue rolling it through to the thickness you want.
Repeat with the other half of the dough. If you’re rolling the dough by hand, put the chunk of dough between 2 pieces of wax paper and roll it with a pin until it’s as thin as possible without breaking—less than 1/16 inch thick.